1943, I did try that. As you may be able to tell from the photo, I took a big piece of butcher paper and drew out the lines into which the diamonds should have fit. I rearranged them every which way and always had at least two that wouldn't fit.
I'm now wondering if I did something wrong from the very beginning-- like when I cut the diagonal strips (from the horizontal) that I cut them too wide.
Mmm... maybe there's a solution there? undo each of the strips and re-measure *those*; when stitched together, shouldn't each of the individual diamonds be "perfect" diamonds, not as "stretched" as they currently are?